Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D431 |
| commutator, socle, cosocle | C22×C431 | C24 |
| Fitting | #124×C431 | C2 |
| prime radical | #28352157 | C2 |
| hypercenter | #124 | D431 |
| hypocenter | C431 | #551 |
| LCS | G ▷ C22×C431 ▷ C431 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28352182 | C2 | semidirect |
| 2. #28352171 | C2 | semidirect |
| 3. #28352170 | C2 | semidirect |
| 4. #28352165 | C2 | semidirect |
| 6. (C22⋊D431)⋊C4 | C2 | semidirect |
| 7. #28352146 | C2 | semidirect |
| 8. C22⋊C4×D431 | C2 | semidirect |
| 9. #124×C431 | C2 | semidirect |
| 12. C22×Dic431 | C22 | semidirect |
| 15. C4⋊Dic431 | C22 | semidirect |
| 16. Dic431⋊C4 | C22 | semidirect |
| 17. Dic431⋊C4 | C22 | semidirect |
| 18. Dic431⋊C4 | C22 | semidirect |
| 21. C22⋊Dic431 | C22 | semidirect |
| 25. C4×Dic431 | C22 | semidirect |
| 26. C2×Q8×C431 | C22 | semidirect |
| 29. C22⋊C4×C431 | C22 | semidirect |
| 30. C42×C431 | C22 | semidirect |
| 68. C431 | #551 | semidirect |
| 71. #124 | D431 | semidirect |
| 80. C2×Q8 | C2×D431 | semidirect |
| 97. C22⋊C4 | C2×D431 | semidirect |
| 99. C42 | C2×D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352182 | 2 |
| #28352171 | 2 |
| #28352170 | 2 |
| #28352165 | 2 |
| #28352157 | 2 |
| (C22⋊D431)⋊C4 | 2 |
| #28352146 | 2 |
| C22⋊C4×D431 | 2 |
| #124×C431 | 2 |
| #551 | 431 |